On whitham equations for camassa-holm
Web25 de nov. de 2024 · The nonlinear Schrödinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude‐frequency domains. In… 13 PDF View 2 excerpts, references methods Multiphase averaging and the inverse spectral solution of the Korteweg—de … WebWe study the generalized Camassa-Holm equation which contains the Camassa-Holm (CH) equation and Novikov equation as special cases with the periodic boundary condition. We get a blow-up scenario and obtain the global existence of strong and weak solutions under suitable assumptions, respectively. Then, we construct the periodic peaked …
On whitham equations for camassa-holm
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WebCamassa and Holm [1993] recently derived a new dispersive shallow water equation known as the Camassa–Holm equation. ... Periodic Wave Solutions and Their Asymptotic Property for a Modified Fornberg–Whitham Equation. Yiren Chen. 15 September 2024 Symmetry, Vol. 12, No. 9. Web28 de fev. de 2024 · We determine the stability and instability of a sufficiently small and periodic traveling wave to long wavelength perturbations, for a nonlinear dispersive equation which extends a Camassa-Holm equation to include all the dispersion of water waves and the Whitham equation to include nonlinearities of medium amplitude waves. …
WebModulation of Camassa--Holm equation and reciprocal transformations Abenda, Simonetta ; Grava, Tamara We derive the modulation equations or Whitham equations for the Camassa--Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure. WebThe Camassa–Holm equation has a number of constants of motion arising as eigenvalues of an associated spectral problem. ... Yang S (2024) Wave Breaking Phenomena for the Fornberg–Whitham Equation, Journal of Dynamics and Differential Equations, 10.1007/s10884-020-09866-z, 33:4, ...
Web1 de jun. de 2024 · In this paper, we investigate the generalized Camassa–Holm equation with k + 1 degree nonlinearities. The global existence is established, provided that 0 < b < k and the initial data y0= (1−∂x2)u0 do… Expand Save Alert Large Time Behavior of Momentum Support for a Novikov Type Equation Caochuan Ma, Yaqiang Cao, … WebWe apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Camassa–Holm equation for decaying initial data, completing previous results by …
Web15 de nov. de 2007 · These Whitham equations are quasilinear hyperbolic equations and they describe the averaged dynamics of the rapid oscillations which appear in the … clinton lewis eastman gaWeb1 de set. de 2009 · In this paper we take up the question of a small dispersion limit for the Camassa-Holm equation. The particular limit we study involves a modification of the Camassa-Holm equation, seen in the recent theoretical … clinton lewis agrofreshWeb5 de out. de 2024 · It is interesting that the FW equation does not only allow traveling wave solutions like the KdV equation, but also possess peakon solutions [11] as some Camassa–Holm type equations. However, the FW equation is not integrable [20] and there is no useful conservation laws which would be used to make estimates of solutions, … bobcat crusherWebWell-posedness of higher dimensional Camassa-Holm equations on manifolds with boundary Fran¸cois Gay-Balmaz1 AMS Classification: 37K65, 35Q35, 35Q53, 58D05, 58B20, 53D25. Keywords: Camassa-Holm equations, well-posedness, Sobolev diffeomorphism group, weak Riemannian metrics, geodesic spray, Euler-Poincar´e … bobcat cross with domestic catWeb5 de nov. de 2024 · More specifically, we will now focus on the Cauchy problem for the periodic higher-order Camassa–Holm equations, i.e.(1.3){mt+(u2−ux2)p−1uxm+(u(u2−ux2)p−1m)x=0,t>0,x∈S,u(0,x)=u0(x),x∈S,where S=R/Z=[0,1)is the unit circle, and aim to leverage ideas from our previous work to further … clinton lewinsky comicWeb15 de nov. de 2006 · We present a Riemann–Hilbert problem formalism for the initial value problem for the Camassa–Holm equation u t − u t x x + 2 ω u x + 3 u u x = 2 u x u x x + … clinton lewinsky hearingWeb2 de mai. de 2007 · We survey some topics involving the Whitham equations, concentrating on the role of ψψ ∗ (or square eigenfunctions) in averaging, where ψ is the … bobcat cry